Related papers: Statistics on $\ell$-interval parking functions
We prove the property that a function is cyclic (resp., non-cyclic) is not preserved by norm convergence in Dirichlet-type spaces $D_\alpha$, and show how other significant quantities for cyclicity do remain preserved under the limit of…
This paper describes a smart parking sensing and information system that disseminates the parking availability information for public users in a cost-effective and efficient manner. The hardware framework of the system is built on advanced…
In 2000, it was demonstrated that the set of $x$-parking functions of length $n$, where $x$=($a,b,...,b$) $\in \mathbbm{N}^n$, is equivalent to the set of rooted multicolored forests on [$n$]=\{1,...,$n$\}. In 2020, Yue Cai and Catherine H.…
We study the kinetics of competitive random sequential adsorption (RSA) of particles of binary mixture of points and fixed-sized particles within the mean-field approach. The present work is a generalization of the random car parking…
Understanding user's perception of service variability is essential to discern their overall perception of any type of (transport) service. We study the perception of waiting time variability for ride-hailing services. We carried out a…
Statistical mechanics of a disordered system of cars on a single-lane road is developed. Behaviour of cars is defined by conditional probability of car velocity depending on the distance and velocity of the car ahead. A system consisting of…
Let $W$ be a Weyl group with root lattice $Q$ and Coxeter number $h$. The elements of the finite torus $Q/(h+1)Q$ are called the $W$-{\sf parking functions}, and we call the permutation representation of $W$ on the set of $W$-parking…
A defective $(m,n)$-parking function with defect $d$ is a parking function with $m$ cars attempting to park on a street with $n$ parking spots in which exactly $d$ cars fail to park. We establish a way to compute the defect of a defective…
The paper addresses the Vehicle Relocation Problem in free-floating car-sharing services by presenting a solution focused on strategies for repositioning vehicles and transferring personnel with the use of scooters. Our method begins by…
We give a complete description of the behaviour of the sequence of displacements $\eta_n(z)=\Phi^n(x) - \Phi^{n-1}(x) \ \rmod \ 1$, $z=\exp(2\pi \rmi x)$, along a trajectory $\{\varphi^{n}(z)\}$, where $\varphi$ is an orientation preserving…
Public road authorities and private mobility service providers need information derived from the current and predicted traffic states to act upon the daily urban system and its spatial and temporal dynamics. In this research, a real-time…
Parking functions are a widely studied class of combinatorial objects, with connections to several branches of mathematics. On the algebraic side, parking functions can be identified with the standard monomials of $M_n$, a certain monomial…
Mixable loss functions are of fundamental importance in the context of prediction with expert advice in the online setting since they characterize fast learning rates. By re-interpreting properness from the point of view of differential…
The increasing availability and adoption of shared vehicles as an alternative to personally-owned cars presents ample opportunities for achieving more efficient transportation in cities. With private cars spending on the average over 95\%…
Traffic breakdown, as one of the most puzzling traffic flow phenomena, is characterized by sharply decreasing speed, abruptly increasing density and in particular suddenly plummeting capacity. In order to clarify its root mechanisms and…
In this paper, we introduce the concept of the $\alpha$-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers. Also, we study some properties of such fractal…
In this paper we analyze the spatial distribution of elements around points of interest. Based on a spatial exclusion principle we model the system by means of a Fermi-Dirac distribution defined by two easily interpretable parameters. By…
We introduce a rather natural family of non-uniform distributions on $PF_n$, $n\in\mathbb{N}$, the set of parking functions of length $n$. One of the motivations for this comes from a similar situation in the context of integer partitions.…
Understanding the mechanisms responsible for the emergence and evolution of oscillations in traffic flow has been subject to intensive research by the traffic flow theory community. In our previous work, we proposed a new mechanism to…
We introduce type C parking functions, encoded as vertically labelled lattice paths and endowed with a statistic dinv'. We define a bijection from type C parking functions to regions of the Shi arrangement of type C, encoded as diagonally…